Dr. Anthony Fauci, the nations leading expert on infectious diseases, told the Senate Health Committee on Tuesday that the true coronavirus death toll is likely higher than what has been reported so far and cautioned Americans that going back to normal life too soon could lead to major spikes in cases.

I dont know the exact precent that its higher, but certainly, its higher, Fauci said of the death toll in response to a question from Sen. Bernie Sanders (I-Vt.).

If you think we have it completely under control, we dont, he said later, contradicting President Donald Trump s previous assertion that the virus is well contained .

I think were going in the right direction, but the right direction does not mean we are in control, he told Sen. Elizabeth Warren (D-Mass). Failing to respond in an adequate way would without a doubt result in a resurgence of the virus in the fall, Fauci said.

The U.S. death toll stands at nearly 81,000 deaths so far, with more than 1.3 million infections.

More people have probably died of the virus in New York City in particular, Fauci said, considering the extent the citys health care system has been bogged down.

There may have been people who died at home who did have COVID who were not counted as COVID because they had not gotten to the hospital, he said.

Fauci, as well as CDC Director Robert Redfield, FDA Commissioner Stephen Hahn and Assistant Secretary for Health Adm. Brett Giroir, answered senators questions on the federal governments response to the crisis in a session conducted largely via remote videoconferencing.

The public health officials said a COVID-19 vaccine will probably not be ready by the fall, but Fauci is cautiously optimistic that one or more of the eight vaccines currently in development will be proven effective. Vaccine trials have moved so swiftly that Fauci expects to know by late fall or early winter whether they are successful.

Researchers are looking at several antiviral treatments in addition to remdesivir, the one drug recently granted emergency approval for use in hospitalized patients. Plasma treatments are also being researched, as it is believed that plasma from people who have recovered can help people still suffering from the viruss effects.

With widespread testing and contact tracing, the officials hope states will be able to prevent new outbreaks as they work toward reopening economies and sending students back to class in the fall.

But Fauci strongly cautioned against failing to take seriously the guidelines put out by the White House coronavirus task force, which stipulate that states should see a 14-day decline in new cases before loosening restrictions. Several states, including Georgia and Tennessee, have been relaxing restrictions for weeks without having met that first milestone.

If leaders reopen local economies too quickly, Fauci said, the consequences could be really serious.

At one point, Sen. Rand Paul (R-Ky.) pushed back against the overall message of caution, saying that rural states that have not yet seen major outbreaks and their school districts, in particular should be exempt from the national strategy.

As much as I respect you, Dr. Fauci, I dont think youre the end-all, Paul said, arguing that the impact of coronavirus outside of New England has been benign.

I never made myself out to be the end-all and the only voice in this, Fauci responded. Im a scientist, a physician and a public health official.

Fauci stressed that school systems should exercise caution in reopening. In recent weeks, rare and dangerous inflammatory symptoms linked to the virus have been seen in children some of whom have died.

I think weve got to be careful if we are not cavalier in thinking that children are completely immune to the deleterious effects, he said.

Fauci added: I dont know everything about this disease, and thats why Im very reserved in making broad predictions.

The disease experts message generally conflicted with that of the White House and Trump, who warned about the risk of permanent economic damage and additional suicide deaths associated with broad coronavirus restrictions.

Paul continued to make the case after the hearing that the country should begin to reopen, including by allowing children to go back to school.

We ought to consider mortality in children virtually zero. We should get our kids back in school. I also dont think you need a gazillion tests, Paul said.

While most cases of coronavirus in kids are mild, experts worry that allowing children to go back to school risks them possibly bringing the disease home to more vulnerable family members.

Igor Bobic contributed to this report.